Chapter 2 – Elementary Cryptography
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 Concepts
of encryption
 Cryptanalysis
 Symmetric (secret key) Encryption
 Asymmetric (public key) Encryption
 Key exchange protocols and certificates
 Digital Signatures
 Cryptographic hash functions
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Sender (S), Recipient (R), Transmission
media (T)
Interceptor / intruder (O) (availability)
O might block message from reaching R
O might intercept message (confidentiality)
O might modify message (integrity)
O might fabricate an authentic-looking
message (integrity)
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Encryption – process of encoding a message
Decryption – transforming encoded
message back to normal
Encrypt – encode , encipher
Decrypt – decode, decipher
Cryptosystem – system for encryption and
decryption
Plaintext – original form of message
Ciphertext – encoded form of message
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Algorithms – rules for encryption and decryption
Key – value used to encrypt message
C = E(K, P) where P=plaintext, K = key, E = encryption algorithms, and
C = ciphertext
Symmetric encryption P = D(K, E(K,P))
Asymmetric encryption P = D(KD, E(KE,P))
Keyless cipher
Cryptography (hidden writing) – uses encryption to hide
message
Cryptanalysis – attempts to find meanings in encrypted
messages
Cryptology – study of encryption and decryption
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Sometimes the encryption and decryption keys are
the same
P = D (K, E (K, P))
where P=plaintext, K = key, E = encryption algorithms, and C
= ciphertext
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At other times, encryption and decryption keys
come in pairs
Decryption key, KD
Encryption key KE
P = D (KD, E (KE, P))
where P=plaintext, K = key, E = encryption algorithms, and
C = ciphertext
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Cryptography (secret writing) is the strongest
tool for controlling against many kinds of
security threats.
Well-disguised data cannot be read, modified,
or fabricated easily. Cryptography is rooted in
higher mathematics: group and field theory,
computational complexity, and even real
analysis, not to mention probability and
statistics. Fortunately, it is not necessary to
understand the underlying mathematics to be
able to use cryptography.
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Attempt to break a single message
Attempt to recognize patterns in encrypted
messages
Attempt to infer some meaning without
breaking the encryption
Attempt to realize the key
Attempt to find weaknesses in the
implementation or environment of use of
encryption
Attempt to find general weaknesses in an
encryption algorithm
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Cryptographer
A cryptographer works on behalf of a legitimate
sender or receiver
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Cryptanalyst
A cryptanalyst works on behalf of an unauthorized
interceptor
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An encryption algorithm is called breakable
when, given enough time and data, an
analyst can determine the algorithm
May be impractical
A 25-character message of just uppercase
letters has 2625 (1035) possible
decipherments. A computer performing
1010 operations/sec would take 1011 years
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we use the convention;
plaintext is written in UPPERCASE letters,
and ciphertext is in lowercase letters
LASANTHA
11018131970
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A+3=D
N-1 =?
C+10 = ?
S+9=?
X+4=?
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Substitution – one or more characters are
replaced with another
Transpositions (permutations) – order of
characters is rearranged
Hybrid – combinations of the two types
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This technique is called a monoalphabetic
cipher or simple substitution
A substitution is an acceptable way of
encrypting text
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Each letter is translated a fixed number of
positions in the alphabet
Ci = E(pi) = pi + 3 (Caesar used a shift of 3)
Easy to perform; easy to break
Look for double letters and then use common
words with double letters
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Use a key to scramble the letters
ABCDEFGHIJKLMNO…
c i ph ers abdfgj kl …
Rearrange using a fixed distance between
letters (e.g. every 3rd)
ABCDEFGHIJKLMNO…
adg j mpsvybehkn r…
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Substitution encryption algorithms can be
performed by direct lookup in tables.
An important issue in using any cryptosystem
is the time it takes to turn plaintext into
ciphertext, and vice versa.
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The techniques described for breaking the
Caesar cipher can also be used on other
substitution ciphers
Look for short words, words with repeated
patterns, common first and last letters
Can use our knowledge of language
Look at frequency distributions
Could reduce time to hours
Nature and context of the text being analyzed
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The pad consists of a large number of
pages where each page contains a nonrepeating key
The sender would write the keys above the
message (e.g. a 300 character message
would require 30 pages of 10 character
keys)
The message is scrambled using a Vigenere
tableau built from the message and key
Problem is synchronizing the receiver’s pad
with the senders pad
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I am, I exist, that is certain.
uaopm kmkvt unhbl jmed
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One-time pad consists of an arbitrary long
non-repeating sequence of numbers that
are combined with the plaintext
Each plaintext character is represented by
its numeric equivalent and is added to one
of the random numbers. The ciphertext
character is computed from the sum mod
26
Repeated characters are typically
represented by different ciphertext
characters
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Uses a passage from a book to form the
letters at the top of a Vigenere Tableau
Computes ciphertext character by taking
the intersection of the plaintext character
and corresponding character at that
position from the book passage
Relatively easy to break using frequency
distributions
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Columnar Transposition rearranging
plaintext message into columns and then
reading it row by row
Transposition algorithms require a constant
amount of time per character and are (n)
algorithms, but space required to store
results and delay in waiting for all
characters to be read are dependent on the
size of the plaintext
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THIS IS A MESSAGE TO SHOW HOW A COLUMNAR
TRANSPOSITION WORKS
tssoh oaniw haaso lrsto imghw utpir seeoa
mrook istwc nasns
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If the message length is not a multiple of the
length of a row, the last columns will be one
or more letters short. When this happens, we
sometimes use an infrequent letter, such as
X, to fill in any short columns
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Compute letter frequencies of ciphertext; if
appear with normal frequency, then assume a
transposition algorithm was used
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The amount of secrecy needed should determine
the amount of labor appropriate for the encryption
and decryption
The set of keys and the enciphering algorithm
should be free from complexity
The implementation of the process should be as
simple as possible
Errors in ciphering should not propagate and cause
corruption of further information in the message
The size of the enciphered text should be no larger
than the text of the original message
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Most of the ciphers we have presented so far are
stream ciphers (exception is the columnar
transposition cipher)
convert one symbol of plaintext immediately into a
symbol of ciphertext
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Skipping a character in the key during
encryption
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A block cipher encrypts a group of plaintext
symbols as one block
Eg: columnar transposition
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Advantages and
disadvantages of
stream and block
encryption algorithms
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The interceptor should not be able to predict
what will happen to the ciphertext by
changing one character in the plaintext
The goal of substitution is confusion
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The cipher should also spread the
information from the plaintext over the entire
ciphertext so that changes in the plaintext
affect many parts of the ciphertext
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Charles P. Pfleeger, (2005) "Security in
Computing (Fourth Edition)", Prentic-Hall
International, Inc.
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thank you
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